Highest Common Factor of 9670, 9205, 12327 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 9670, 9205, 12327 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9670, 9205, 12327 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 9670, 9205, 12327 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 9670, 9205, 12327 is 1.
HCF(9670, 9205, 12327) = 1
HCF of 9670, 9205, 12327 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9670, 9205, 12327 is 1.
Highest Common Factor of 9670,9205,12327 is 1
Step 1: Since 9670 > 9205, we apply the division lemma to 9670 and 9205, to get
9670 = 9205 x 1 + 465
Step 2: Since the reminder 9205 ≠ 0, we apply division lemma to 465 and 9205, to get
9205 = 465 x 19 + 370
Step 3: We consider the new divisor 465 and the new remainder 370, and apply the division lemma to get
465 = 370 x 1 + 95
We consider the new divisor 370 and the new remainder 95,and apply the division lemma to get
370 = 95 x 3 + 85
We consider the new divisor 95 and the new remainder 85,and apply the division lemma to get
95 = 85 x 1 + 10
We consider the new divisor 85 and the new remainder 10,and apply the division lemma to get
85 = 10 x 8 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 9670 and 9205 is 5
Notice that 5 = HCF(10,5) = HCF(85,10) = HCF(95,85) = HCF(370,95) = HCF(465,370) = HCF(9205,465) = HCF(9670,9205) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 12327 > 5, we apply the division lemma to 12327 and 5, to get
12327 = 5 x 2465 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 12327 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12327,5) .
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Frequently Asked Questions on HCF of 9670, 9205, 12327 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 9670, 9205, 12327?
Answer: HCF of 9670, 9205, 12327 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9670, 9205, 12327 using Euclid's Algorithm?
Answer: For arbitrary numbers 9670, 9205, 12327 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.